Deterministic entanglement between non-interacting systems with linear optics

Measurement-based heralded entanglement schemes provide the primary method to entangle physically separated nodes in most quantum systems. However, the impossibility of performing a deterministic Bell measurement with linear optics bounds the success rate of these protocols to at most 50%. Here we show that the ability to perform feedback during the measurement process enables unit success probability in a single shot. Our primary feedback protocol, based on photon counting, retains the same robustness as the standard Barrett-Kok scheme, while doubling the success probability even in the presence of loss. Furthermore, it generalizes to creation of distributed $N$-particle Dicke states. In superconducting circuits, for which homodyne detectors are more readily available than photon counters, we give another protocol that can deterministically entangle remote qubits given realistic parameters. In constructing the latter protocol, we derive a general expression for locally optimal control that applies to any continuous feedback problem.